Oil Velocities Research Articles

Exploring the correlation between inclination angle and flow pattern transition in oil-water flow

The impact of pipe inclination angle on oil-water flow regimes transition boundaries is vital in various engineering applications, including pipeline and separator inlet design. Understanding this influence is crucial for identifying alternative and optimal designs. The standard way of presenting oil and water superficial velocities on 2D flow pattern maps doesn't consider how the flow pattern varies with pipe tilt angle. This article aims to clarify how the angle of pipe inclination affects oil-water flow regime transitions. This method uses pipe inclination angle as a direct representation, with the angle shown on the x-axis of a 2D flow pattern map, which has not been done before in literature. The y-axis, or ordinate, is a dimensionless number that accounts for mixture velocity, fluid densities, and pipe diameter. Two dimensionless numbers were utilized. The Froude number based on mixture velocity, FrM, and the Reynolds number (ReOM) based on mixture velocity and oil properties, are plotted against pipe inclination angle. The evaluation and validation of the proposed methods for the effect of the inclination angle were performed using a database of more than 10,000 points established from studies reported in the literature. The findings show that both the Dispersed (DF) and Semi-Dispersed flow regimes (SDF) exhibit higher FrM values than smooth stratified regardless of the pipe's incline. Moreover, the spreading area is symmetric around the horizontal line which means that the DF and SDF can be observed at similar FrM for both positive and negative inclinations. Focusing horizontally, FrM is highest for ST-MI, lower for SW, and lowest for ST. This paper also presents and demonestrates a case study showcasing a new application for flow pattern maps, illustrating their potential in design purposes.

Numerical Studies On the Oil Film Thickness in the Case of Stratified Flow with Different Oil-Water Flow Combinations Through Sudden Contraction Tube

Abstract Most of the oil transportation industries deal with liquid-liquid flow considering the adiabatic situation. In such applications, film thickness measurement plays a very significant role in understanding the flow characteristics. The distribution of phases for efficient wall treatment and to understand the phase distribution, measurement of film thickness is very important. Among different flow patterns, stratified flow is most common for low and medium viscous oil-water flow. At lower oil velocities, stratified flow is observed downstream of singularity whereas in the upstream section, stratified flow is observed for low to medium oil velocities and high-water superficial velocity. Variation of oil film thickness for stratified flow has been analyzed in the present study. Results show that oil film thickness decreases with the increase in the superficial velocity of water (Us-Water) for a constant oil superficial velocity (Us-Oil). With the increase in the volume fraction of one phase, the film thickness of that phase increases. As Us-Oil increases, the film thickness of oil also increases for a constant Us-Water. Oil film thickness is directly proportional to the viscosity of oils. This means, the more the viscosity of the oil, the more will be the oil film thickness.

Analysis of Core Annular Flow Behavior of Water-Lubricated Heavy Crude Oil Transport

A possible method for fluid transportation of heavy oil through horizontal pipes is core annular flow (CAF), which is water-lubricated. In this study, a large eddy simulation (LES) and a sub-grid-scale (SGS) model are used to examine CAF. The behavior of heavy oil flow through turbulent CAF in horizontal pipes is numerically investigated. The Smagorinsky model is utilized to capture small-scale unstable turbulent flows. The transient flow of oil and water is first separated under the behavior of the core fluid. Two different conditions of the horizontal pipes, one with sudden expansion and the other with sudden contraction, are considered in the geometry to investigate the effects of different velocities of oil and water on the velocity distribution, pressure drop, and volume fraction. The model was created to predict the losses that occur due to fouling and wall friction. According to the model, increasing water flow can reduce fouling. Additionally, the water phase had an impact on the CAF’s behavior and pressure drop. Also, the increased stability in the CAF reduces the pressure drop to a level that is comparable to water flow. This study demonstrated that a very viscous fluid may be conveyed efficiently utilizing the CAF method.

Experimental investigation of viscous oil–water–sand flow in horizontal pipes: Flow patterns and pressure gradient

Fluid production from unconsolidated reservoirs often leads in sand production, which poses a number of issues. Sand deposition in flowlines can result in significant pressure dips, pipe and facility damage, and obstructions that decrease productivity. More research is needed to understand the movement and deposition of sand in oil–water–sand (O–W–S) fluxes. This article focuses on O–W–S flows in a 6-meter-long horizontal pipe with an inner diameter of 0.0381 m. The study looks at the flow behavior of high viscosity oil–water (O–W), water–sand (W–S), and oil–water–sand (O–W–S) flows. Experiments were carried out at 250 psig pressure in a laboratory flow test facility using various heavy synthetic oils (viscosities ranging from 3500 cP to 7500 cP at 25°C) and tap water. The sand concentration varied from 1% to 10%, with an average sand particle diameter of 145 μm and material density of 2630 kg/m3. Water cuts ranged from 0.0 to 1.0. The experimental results revealed a minor change in pressure gradient between (O–W) and (O–W–S) flows. However, increasing the sand concentration in (O–W–S) flow resulted in higher pressure losses. The reduction factor of pressure gradient indicated that the highest decrease in pressure drop occurred at higher superficial oil velocities. Furthermore, a direct relationship was observed between the reduction factor and the decrease in water cut. The results also showed that the minimum required transportation velocity for sand slurry decreased with increasing superficial oil velocity, while the minimum transportation condition increased with higher sand concentration. The comparison between the expected pressure gradient from Bannwart and McKibben et al. and the actual experimental data demonstrated significant accuracy for the oil viscosities and superficial oil velocities used in the study.

Droplet splitting in multi‐furcating microchannel: A three‐dimensional numerical simulation study

AbstractThis work investigates the splitting of a droplet in a multi‐furcating microfluidic channel for a two‐phase system employing 3D simulation. The simulations were performed using an explicit volume of fluid (VOF) method and have been validated using experimental data taken from the literature. The width ratio of the branch channel to the main channel is set to 0.25 for five branches of the multi‐furcating microchannel, as it is the width ratio at which multiple splitting takes place. Simulations have been carried out at different oil velocities (Vo) ranging from 0.12 to 0.22 m/s and at different water velocities (Vw) ranging from 0.002 to 0.10 m/s. Oil fraction data in the main channel has been recorded and compared with the homogenous model. The average difference between the homogeneous model and the 3D simulations is 22.68%. Analysis of dimensionless droplet length in ±0°, ± 40°, and 90° branch channels has been done. α (length of the droplet in branch channel/width of the main channel) increases up to a flow rate ratio of 0.38, and then decreases, whereas β (length of the droplet in the main channel/width of the main channel) increases with an increase in flow rate ratio. A flow pattern map has been developed to identify the various droplet breakup regimes at the junction. Frequency (counts per unit time) of droplet generation increases with capillary number for all the branch channels except for the 0° branch channel, where the regime is that the droplet passes through three branch channels. The volume distribution ratio (λ) decreases at first, then increases with an increase in capillary number for 0°:90° and 40°:90° angle branch channels for the regime where the droplet passes through five branch channels. For the regime where the droplet passes through three branch channels, the trend is likely linear with λ = 0.3 ± 0.04. The dimensionless mother droplet length increases with an increase in capillary number for Vo = 0.13 and 0.16 m/s, but for Vo = 0.19 and 0.22 m/s, the dimensionless mother droplet length becomes constant after capillary number = 0.26 and 0.30 respectively. The droplet breakup time (t) for regime (a), where the droplet passes through three branch channels, is 0.002 s; for regime (b), where the droplet passes through five branch channels, it is 0.001 s; and for regime (c), where multi‐furcation and coalescence of the droplet occurs, it is 0.0005 s. Multiple splitting is a topic covered in this paper that can be applied to upcoming microfluidic platform‐based devices.

Study on the Hydrodynamic Performance and Stability Characteristics of Oil-Water Annular Flow through a 90° Elbow Pipe

The transportation of highly viscous oil surrounded by water annulus has been recognized as a feasible option in terms of low-energy consumption and high efficiency. During the process of heavy oil delivery, the problem of pipe fittings is inevitably encountered, and the most common one is elbow assembly. In this present study, simulations for oil-water core annular flow (CAF) through a 90° elbow pipe were performed by computational fluid dynamics (CFD) based on VOF, standard k-ε, and CSF models. Simulation results were consistent with experimental data, which verifies the validity and practicability of the proposed model. The effects of inlet water fraction, superficial velocities of oil and water, oil properties (density and viscosity), and pipe geometry-related parameters (diameter ratio, wall roughness, and surface wettability) on the hydrodynamic performance and stability characteristics were explored. It is revealed that inlet water fraction, superficial velocities of oil and water, oil properties, and pipe geometric parameters do influence the volume fraction of oil and the stability of the water ring. Furthermore, the oil core may adhere to the downstream of the 90° elbow pipe under certain operational conditions. The results could provide a reference for the design of 90° elbow pipe structures and the optimization of operation parameters.

Effect of the down-slope on the structure and the pressure loss of an oil-water stream

The methodology and the results of an experimental campaign aimed at characterizing a two-phase flow of an oil-water-mixture in downward inclined pipes are here described. The goal was to assess the effects of the downslope on an oil-water stream in terms of flow patterns, pressure gradients and phase holdup inside a 40 mm I.D. pipe. The experiments ranged within (0.56−1.06ms) and (0.66−1.33ms) oil and water superficial velocities, respectively. The transition from annular to stratified-wavy flow pattern was analyzed and showed to occur at lower oil velocities with respect to the horizontal configuration. The frictional pressure gradients were measured, the results compared to mechanistic and empirical models showed to be in good agreement. The phase holdups were measured by quick-closing valves and compared to horizontal configuration results and literature models. Eventually, the drift-flux model was implemented confirming its applicability and a relationship for the of oil holdup was derived.

Measurement of Liquid–Liquid Flows Using Turbine Flowmeter and Conductance Sensor With Multiheight Electrodes in Vertical Pipes

Liquid–liquid two-phase flows are common industrial processes in chemical, petroleum, and other related fields. It is a great challenge for the flow measurement using the turbine flowmeter (TFM) in low-velocity liquid–liquid flows due to the serious slippage effect between the oil and water phases. The complex physical discrepancies between the two phases make the response of TFM vastly different from that in single-phase flow. This study proposes a system combining TFM and conductance sensors with multiheight electrodes (CSMHEs) to determine liquid–liquid two-phase flows. This study investigates the effects of phase distribution and slippage on the wheel hub drag torque. The model of wheel hub drag torque in different flow patterns is established, and a new variable meter factor model of TFM in liquid–liquid flows is constructed. Experiments in 20-mm simulated well reveal that the TFM can make accurate predictions of total flow rate and enable online measurements of individual phase superficial velocities. The absolute average percentage deviations (AAPDs) of superficial water and oil velocities are 2.01% and 7.24%, respectively.

Study on the migration law of CO2 miscible flooding front and the quantitative identification and characterization of gas channeling

CO2 miscible flooding can significantly improve crude oil recovery in low permeability reservoirs. At present, research on the migration process of CO2 miscible flooding has mainly focused on the characterization of CO2 concentrations at different locations and the characterization of oil and gas migration velocities, but there have been few quantitative characterization studies on the migration law of CO2 miscible flooding front and the identification of gas channeling time. In view of the above problems, considering the effects of reservoir physical properties, injection parameters and migration mechanisms on the front migration of CO2 miscible flooding, a mathematical model of CO2 miscible flooding is established. Based on the characterization of the CO2 front and miscible zone front, the effects of porosity, initial injection concentration, dispersion and adsorption on the migration law of the CO2 miscible flooding front and gas channeling time are analyzed. The results show that during the migration of CO2, the entire flow area is divided into the CO2 area, miscible area and crude oil area through the CO2 front and miscible zone front, and the miscible area gradually moves to the production end with the increase in injection volume. When the adsorption is weak, the increase in porosity and initial injection concentration accelerates the mass transfer and dispersion process, and the stronger the dispersion is, the larger the miscible area and the earlier the gas breakthrough time. The enhancement of adsorption reduces the miscible area and delays the complete gas channeling time. This study has significance regarding mines for understanding the migration law of CO2 miscible flooding front and the timing of complete gas channeling in low permeability reservoirs.

Displacing water from a low spot in a pipeline by a turbulent oil flow: Experiments and simulations

Water may accumulate at low sections of oil transportation pipelines. Continuous removal of the water by the oil is essential to avoid possible damages to the pipeline and ensure proper oil flow. Lab-scale experiments were performed to determine the critical oil velocity that enables the removal of accumulated water by turbulent oil flow and to measure the water propagation velocity at supercritical oil velocities. Effects of the riser inclination, initial water volume, and oil flow rate on the oil–water flow phenomena were documented. The data obtained were compared with results of 2D and 3D numerical simulations. The oil viscosity and pipe diameter effects were tested via numerical simulations. More viscous oils have been found to reduce the critical oil velocity and increase water propagation velocities, however with a rather weak effect. The critical oil velocity increases with the pipe diameter and the water propagation velocity is reduced.

Effect of Oil Viscosity on Flow Pattern Transition of Upward Gas-Oil Two-Phase Flow in Vertical Concentric Annulus

Summary Gas-oil two-phase flow usually occurs during gas influx into the wellbore annulus of deepwater drilling with oil-based drilling fluid or gas-oil production from the wellbore annulus. A flow pattern transition often is used in well control or in production parameter design. Related studies primarily have focused on gas-water two-phase flow, which is significantly different from gas-viscosity oil two-phase flow. We conducted experiments on a facility that included a flow section that was 13 000 mm long, with a 60-mm inner pipe and a 100-mm outer pipe in the annulus. A range of oil viscosities from 16 to 39 mPa∙s has been studied. The superficial gas and oil velocities varied from 0.55 to 17.077 m/s and from 0 to 0.414 m/s, respectively. A flow pattern was identified based on visualized analysis using electrical capacitance volume tomography (ECVT) and void faction wave analysis. Flow pattern maps of different viscosities were plotted based on measured data. Transition criteria based on Froude number and Archimedes number were established. The new model was compared with gas-water two-phase flow transition models and validated with experimental data. The effect of viscosity on flow pattern transition was revealed. The transition boundary of the bubble to slug flow and slug to churn flow both moved in the direction of smaller superficial gas velocity with an increase in oil viscosity. There may exist a critical viscosity value when churn flow transited to annular flow. When the viscosity was lower than this critical point, the above result was the same for churn to annular flow when the superficial oil velocity was low. With an increase in the superficial oil velocity, however, the boundary gradually changed to high superficial gas velocity as the oil viscosity increased. When the viscosity was larger than the critical point, the oil viscosity had a slight influence on the transition.

Effects of drag-reducing polymers on the flow patterns, pressure gradients, and drag-reducing rates of horizontal oil–water flows

The effects of drag-reducing polymers on the flow patterns, pressure gradients, and drag-reducing rates of oil–water two-phase flows were investigated using a horizontal acrylic pipe with an inner diameter of 25.4 mm and No. 7 white oil with a viscosity of 10.6 mPa∙s and a density of 888.9 kg/m3 at 25 °C. An aqueous solution of polyacrylamide (PAM), with a molecular weight of 19 million Daltons and a concentration of 100 ppm, was used. In the experiment, the oil and water velocities were 0.1-1.5 m/s and 0.1-1.6 m/s, respectively. The DRPs were found to extend the transition boundaries of stratified flow (ST), ST with mixing at the interface (ST&MI), dispersion of oil in water and water (Do/w&w), and oil and dispersion of oil in water (o&Do/w) but did not change the transition boundaries of dispersion of water in oil (Dw/o). The maximum drag reduction rate could be obtained by adding the DRPs to the dispersion of oil in water (Do/w). The drag reduction effect was closely related to the oil and water velocities. An empirical model for the friction factor was established.

Numerical quasi-three dimensional modeling of stratified oil-water flow in horizontal circular pipe

The stratified oil-water two-phase flow is commonly encountered in offshore oil production systems, and is considered to be among the fundamental flow configuration in two-phase systems. A numerical quasi-three dimensional model for the calculations of the axial pressure gradient, interface height, water holdup, and the flow field in a fully developed oil-water two-phase stratified pipe flow has been developed. The oil-water curved interface configuration is predicted by using minimum energy model. The model solves the governing equations of the steady axial momentum and mass conservation equations together with a low Reynolds number k～ε model of turbulence for the eddy viscosity, performed in the bipolar coordinate system, for convenient describing the curved interface and mapping of the physical domain. The predicted dynamic parameters, such as interface height of close to the pipe wall and in the middle of the pipe cross-section, water holdup, pressure gradient and flow filed are compared with the experiments. At the same time, this model is utilized to study the variation of these dynamic parameters with increasing superficial oil and water velocities. In addition, the numerical model with concave oil-water interface gives more accurate results than a flat interface. It indicates that the interfacial configuration effects are significant.

Investigation on drag reduction of aqueous foam for transporting thermally produced high viscosity oil

An innovative idea is proposed for facilitating the transportation of thermally produced high-viscosity oil by injecting temperature tolerant aqueous foam. To this aim, experimental investigations of the flow characteristics of heated highly viscous oil flowing through a 25 mm i.d. horizontal rough-wall tempered borosilicate glass pipe were conducted. Measurements were made for the superficial oil and foam velocities in the range of 0.05–0.40 m/s and 0.04–0.39 m/s, respectively. Eccentric core annular flow configurations detected by a high-speed camera were found to be particularly dominant throughout the entire tested range. A two-fluid, three-zone mechanistic model for horizontal foam-oil flows was implemented for the case of shear thinning power-law fluid in the annulus, which is in accordance with the foam rheological behavior at the tested elevated temperature. Good agreement was achieved between the predicted and measured data over a wide range of operational conditions. When a complete foam annulus encapsulating the oil core is formed, a critical value of input foam volume fraction can be determined for the maximum drag reduction ratio. An optimal oil core-to-pipe radius ratio range was determined for the highest oil-transport operational coefficient. The drag reduction performance of the tested hot oil-foam system is better than that obtained with the oil-foam system employed at room temperature.

Measurement of Oil–Gas–Water Flows in Vertical Pipes Using Electromagnetic Flowmeter and Dual-Conductance Sensors

Three-phase flows are significantly complicated in comparison to single-phase flows and gas–liquid two-phase flows. So far, faced with the presence of two nonconductive dispersed phases in oil–gas–water three-phase flows, the measurement characteristics of electromagnetic flowmeter (EMF) in three-phase flows are an unresolved problem. The flowrate of three-phase flows is difficult to measure due to the nonuniformity arising from interactions between dispersed phases. Aiming at the difficult problem of production logging in oil wells of three-phase flows, this article reports an experimental study on measuring three-phase flows via the EMF and the dual-conductance sensors. Among them, the phase holdups of three-phase flow in vertical pipe are extracted through newly designed distributed coaxial double-ring conductance sensor (DRCS) and rotating electric field conductance sensor (REFCS). A three-phase flow loop test in a pipe of 20 mm inner diameter is carried out. The results show that the EMF has the ability to substantively measure the flowrate of water phase under three flow patterns (bubble, slug, and churn flows) when the water cut is above 60%, and the average absolute percentage deviation (AAPD) for prediction of superficial water velocity is 3.55%. The measurement of superficial gas and oil velocities is implemented by solving the drift-flux models of three-phase flow based on the phase holdups and superficial water velocity, and the AAPDs for predictions of superficial gas and oil velocities are 4.33% and 5.95%, respectively. This research provides a new measurement strategy for production logging of oil, gas, and water three-phase flow production profile by combining the EMF with dual-conductance sensors.

Prediction of pressure gradient for oil-water flow: A comprehensive analysis on the performance of machine learning algorithms

Pressure gradient (PG) in liquid-liquid flow is one of the key components to design an energy-efficient transportation system for wellbores. This study aims to develop five robust machine learning (ML) algorithms and their fusions for a wide range of flow patterns (FP) regimes. The MLs include Support Vector Machine (SVM), Gaussian Process (GP), Random Forest (RF), Artificial Neural Network (ANN), k-Nearest Neighbor (kNN), and fusions of these five MLs. A total of eleven hundred experimental data points for nine FPs (two stratified and seven dispersed patterns) in horizontal wellbores are used to develop the MLs. The MLs' performance is evaluated using the metrics including mean absolute percentage error (MAPE), median absolute percentage error (MdAPE), coefficient of variation of root mean squared error (CV-RMSE), and adjusted coefficient of determination. The evaluation metrics are cross-validated using a repeated train-test split strategy. Seven important predictor variables are identified using a supervised feature selection approach: oil and water velocities, FP, input diameter, oil and water density, and oil viscosity. The results show that the high PG prediction accuracy can be achieved using GP compared to other MLs except for the ML-fusions (p < 0.05). A Friedman's test and Wilcoxon Sign-Rank post hoc analysis with Bonferroni correction show that PG prediction errors using GP are significantly lower than using the ANN model (p < 0.05). The values are 18.44 % and 23.9 % for CV-RMSE, 11.6 % and 10.06 % for MAPE, and 7.5 % and 6.75 % for MdAPE, using ANN and GP, respectively. While the previous studies mostly used ANN to demonstrate the capability of MLs to predict PG over the mechanistic or correlation-based models, the present research has shown that GP is even better than ANN using a wide range of FPs and a large data set. • Machine-learning algorithms are developed to predict the pressure gradient. • The Gaussian Process model produces significantly lower prediction error. • The median absolute percentage error using Gaussian Process is 6.75 %. • More than 95 % variation of pressure gradient can be explained using seven variables.

Non-invasive measurement of oil-water two-phase flow in vertical pipe using ultrasonic Doppler sensor and gamma ray densitometer

Oil–water two-phase flow experiments were conducted in a vertical pipe to study the liquid–liquid flow measurement using a non-invasive ultrasound Doppler flow sensor and a gamma-ray densitometer. Tap water and a dyed mineral oil are used as test the fluids. A novel Doppler effect strategy is used to estimate the mixture flow velocity in a vertical pipe based on flow velocity measured by the ultrasound sensor and the shear flow velocity profile model. Drift-flux flow model was used in conjunction phase fractions to predict the superficial velocities of oil and water. The results indicate that the proposed method estimated oil-continuous flow and water-continuous flow have average relative errors of 5.2% and 4.5%; and superficial phase flow velocities of oil and of water have average relative errors of 4.5% and 5.9% respectively. These results demonstrate the potential for using ultrasonic Doppler sensor combined with gamma densitometer for oil–water measurement.

Experimental investigation of oil\u2013water flow in the horizontal and vertical sections of a continuous transportation pipe

A series of experiments were conducted to investigate flow pattern transitions and concentration distribution during simultaneous pipe flow of oil–water two-phase flow through the horizontal and vertical sections. The flowing media applied were white mineral oil and distilled water. Superficial oil and water velocities were between 0 and 0.57 m/s. Flow pattern maps revealed that the horizontal and vertical sections of the pipe lead to different flow pattern characteristics under the same flow conditions. The original contributions of this work are that a transition mechanism for predicting the boundary between oil-in-water (O/W) flow and water-in-oil (W/O) in oil–water two-phase flow was obtained. The effects of input water cut, oil and water superficial velocities on the concentration distribution of the dispersed phase were studied. The empirical formulas for the phase holdup based on the drift-flux model were obtained. The predicted results agreed well with those of the experimental data, especially for the O/W flow pattern.

Experimental Investigation of Oil-Water Two-Phase Flow in Horizontal, Inclined, and Vertical Large-Diameter Pipes: Determination of Flow Patterns, Holdup, and Pressure Drop

Summary Liquid-liquid phase flow in pipes merits further investigation as a challenging issue that has very rich physics and is faced in everyday applications. It is the main problem challenging the fluid flow mechanism in the oil and gas industry. The pressure gradient of liquid flow and flow pattern are still the topics of numerous research projects. In this paper, the emphasis is on further investigation to research the flow pattern, water holdup (HW), and pressure decrease for vertical, horizontal, and inclined flow directions of oil and water flows. Test section lines of 4.19-in. (106.426 mm) inner diameter (ID) and 5-m horizontal, 5-m inclined, and 5-m vertical test sections were serially connected. The experiments were conducted at 40°C using 2-cp viscosity oil and tap water, and oil density of 850 kg/m3, at the standard conditions. Fifty experiments were executed at 250 kPa at the multiphase flow test facility, with horizontal, upward (0.6° and 4°), downward (−0.6° and −4°) hilly terrain and vertical pipes. The oil and water superficial velocities were changed between 0.03 and 2 m/s. This evidence was obtained using video recordings; the flow patterns were observed, and the selection of each flow pattern was depicted for each condition. For horizontal and inclined flow, new flow patterns were documented (e.g., oil transfer in a line forms at the top of the pipeline, typically at high water rate, and water transfer at the lower part of the pipe at a high oil rate). The data were taken at each flow condition, resulting in new holdup and pressure drop. The results show that the flow rate and the pipe inclination angle have major impacts on the holdup and pressure drop performances. In the vertical flow, a clear peak was demonstrated by experiments after the superficial oil velocity reached a certain value. This peak is known as phase inversion point, where after this peak, the pressure starts declining as the superficial oil velocity increases. Also, slippage has been observed after varying inlet oil flow rates between the two phases. The experiments showed that with minor alteration in the inclination angle, the slippage was significantly changed. This study presented new experimental results (measured mainly at horizontal, inclined, and vertical flow conditions) of HW, flow pattern, and pressure drop. These findings are key evidence of the evolving oil-water and flowline estimate models.

Mathematical modelling of hydrothermal performance for Kenics type static mixer using power law obeying fluids

AbstractIn this study, analytical, numerical, and experimental works are presented to demonstrate hydrothermal characteristics of a flow choosing non‐Newtonian behaviour through a Kenics type static mixer. Experiments are conducted by varying the superficial fluid velocities of the heterogeneous mixture oil with Sudan dye and water, as well as for the homogeneous aqueous system, consisting of CMC (2 wt%) in water. Six static mixing elements are placed in series, and the corresponding wall temperatures of the inline pipe are varied over a range of 293–363 K. In the context of hydrodynamic study, analytical models are solved using the Bessel function and Laguerre function and validated with the in‐house experimental results and numerical results. In the thermal performance study, mathematical models are formulated based on differential transformation method (DTM) and homotopy perturbation method (HPM), and have been validated with the numerical results. The deviation among the experimentally measured average pressure drops estimated from our experiment and that predicted by analytical models is found to be as low as ±8.1%. The deviation between the analytical results obtained from the HPM and DTM method and numerical results based on the finite volume method solution of the same equation is observed as low as ±4%. Additionally, both proposed analytical methods used are compared with each other to evaluate the dimensionless swirl flow velocity and temperature gradient of the inline Kenics Static mixer. In the thermal performance study, we observe that the DTM is in good agreement with the numerical method as compared to HPM.